Many construction systems based on frame structures with tetrahedral, hexagonal and/or octagonal modules have been proposed and used. For example, Australian Patent No 475,424 discloses a geodesic space-frame structure of icosahedral shape having pentagonal and hexagonal modules. These modules were themselves formed from isosceles triangles so that the dome-like structure could be cladded with triangular-shaped sheet-material modules. While such geodesic structures (as pioneered by the American inventor Richard Buckmainster Fuller) are essentially dome-like, a great variety of strut-and-node space-frames based on tetrahedral, hexahedral, and octahedral modules are also known and widely used (see, for example Australian patent No 460,682). These are also commonly clad with sheet-material panels of similar modular polygonal shapes, but the cladding panels rarely contribute to the load-bearing capacity of the structure and are not self-supporting.
English architect Arthur Quarmby, and others following his lead (eg, U.S. Pat. No. 4,359,842 to Hooker), proposed a variety of self-supporting structures formed by the pleating or folding of large sheets of material, typically glass-reinforced plastic. Many examples were offered in his book "The Plastics Architect" published by Pall Mall Press, London, 1975. Full structures were formed by unfolding large sheets on-site to form vaults, domes or hutments complete with roofs and walls, the erection process being much like the expansion of bellows. Such structures were tailored individually for their sites and folded for transport. However, the large sheets of material could not be dismantled into smaller modules or components for transport so that, for all but the smallest buildings, on-site construction of the sheets was essential thereby eliminating the advantage of factory production.
U.S. Pat. No. 3,914,486 to Borgford discloses the production of construction panels by pressing a modular hexagonal pattern into a large plate, but such large plates are expensive to press and difficult to handle and transport. U.S. Pat. No. 3,931,697 to Pearce, on the other hand, discloses the use of six different polygonal molecules to form domes and curved structures. The module of most relevance here is a radially pleated, `minimal surface` hexagon in which ridges and valleys do not alternate so that bilateral skewing or `saddling` results. These asymmetric modules are difficult to assemble into structures (requiring five other module types) and cannot be joined together in planar panels, as required for the walls of common rectangular buildings.
U.S. Pat. No. 4,723,382 (and the continuations hereof) to Lalvini discloses a large variety of nodal, periodic and non-periodic, space-frame and panel structures based upon `golden polyhedra` and distortions thereof. The most relevant of these are called `saddle zonogons` and `saddle zonohedra` derived from the radial folding or skewing of plates. Such modules are similar to some of those disclosed by Pearce and suffer from the same disadvantages indicated above.